RU2764781C1 - Method for tracking air target of "turbojet engine aircraft" class under influence of speed and range deception interference - Google Patents

Abstract

FIELD: radio location.

SUBSTANCE: invention relates to the field of digital processing of radar signals and can be used in a radio location station (radar) while tracking an air target (AT) of the "turbojet engine aircraft" class to form reliable identification of combined or separate effects of range and speed deception interference or absence of the effect thereof and to estimate the radial functionally related coordinates (FRC) of mutual displacement of the AT and the radar carrier under different variants of the effect of such interference. The method consists in identifying a combined or separate effect of the range and speed deception interference or the absence of effect thereof and estimating the radial functionally related range to the AT and the speed of approach of the radar carrier thereto by means of an adaptive two-stage parametric approximation (ATPA) of unknown probability densities of phase coordinates by a combination of approximating functions set a priori and approximation of the resulting estimates to the optimal values thereof by considering the nonlinearities in the dynamics of the FRC and the measurements thereof, considering the statistical dependence of the probabilities of changing the variants of the effect of deception interference on the FRC, complexing the radar information and the indicator of the variant of the effect of deception interference, considering the a priori data on changing these variants and adapting the surveillance system thereto. In the method, narrow-band Doppler filtering of the signal reflected from the target is executed using the fast Fourier transformation procedure, Doppler frequency counts associated with reflections of the signal from the airframe and impeller blades of the first stage of the low-pressure compressor of the power plant of the AT are formed, and the formed Doppler frequency counts and output indications of the indicator of the variant of the effect of deception interference are processed in a multichannel filter of combined AT tracking and the first compressor component of the signal spectrum and identification of the variant of the effect of deception interference. Said filter operates in accordance with the procedure for quasi-optimal combined filtering of phase coordinates and recognition of the state of a conditionally Markovian structure of a nonlinear stochastic dynamic system during observation without delay. At the output of the filter, estimates of the conditional probability density of the FRC are formed for a fixed variant of the effect of deception interference.

EFFECT: increase in the reliability of identifying combined or separate effects of range and speed deception interference and estimating the distance to the AT and the speed of approach of the radar carrier thereto.

1 cl, 12 dwg

Description

The present invention relates to the field of digital processing of radar signals and can be used in a radar station (RLS) to form, when tracking an air target (AT) from the class "aircraft with a turbojet engine (TRD)", reliable identification of the joint or separate effects of escaping in range and speed interference or lack of their impact and evaluation of radial functionally related coordinates (FCC) of mutual displacement of the AT and the radar carrier under various options for the impact of such interference.

There is a known method of tracking an AT from the class "aircraft with a turbojet engine" under the influence of noise that leads away in range and speed [1], which consists in the fact that the signal reflected from the target is subjected to narrow-band Doppler filtering based on the Fast Fourier Transform (FFT) procedure and converted to the amplitude-frequency spectrum, the components of which are due to the reflections of the signal from the airframe of the accompanied EC and the rotating blades of the impeller of the low-pressure compressor (LPC) of its power plant, the Doppler frequency reading corresponding to the maximum amplitude of the spectral component of the signal spectrum, which corresponds to its reflections from the airframe of the EC, is determined, and the Doppler frequency reading corresponding to the maximum amplitude of the spectral component of the signal spectrum, located to the right of the Doppler frequency relative to the spectral component of the signal reflected from the airframe of the CC, which are fed to the input of the joint tracking filter of the CC and the first compressor state of the signal spectrum operating in accordance with the procedure (1a)-(6a) of multidimensional linear discrete Kalman filtering in accordance with the equations [1]

where

k=0,1, …, K, …, - number of the filter cycle;

и Р(k+1) - ковариационные матрицы (КМ) ошибок экстраполяции и фильтрации соответственно;

and Р(k+1) - covariance matrices (CM) of extrapolation and filtering errors, respectively;

Φ(k) - state transition matrix;

Q(k+1) and R(k+1) - KM of excitation and observation noise, respectively;

S(k+1) - matrix of weight coefficients; I - identity matrix;

и

- вектор текущих и экстраполированных оценок радиальных ФСК взаимного перемещения носителя РЛС и ВЦ;

and

- the vector of current and extrapolated estimates of the radial FSK of the mutual movement of the carrier of the radar and AT;

H(k+1) - observation matrix;

Y(k) - observation vector;

Z(k+1) - matrix of measurement residuals;

Ψ(k+l) - matrix of a priori filtering errors;

"-1" - the operation of calculating the inverse matrix;

"t" - matrix transposition operation,

между оцененными значениями доплеровских частот, обусловленных отражениями от планера

и лопаток рабочего колеса первой ступени

КНД силовой установки ВЦ, вычисляется модуль производной оценки разности

между оцененными значениями доплеровских частот, который сравнивается с пороговым значением 8, близким к нулю, выполнение или невыполнение условияthe estimate of the difference is determined

between estimated Doppler frequencies due to airframe reflections

and blades of the impeller of the first stage

KND of the power plant of the CC, the modulus of the derivative estimate of the difference is calculated

between the estimated values of the Doppler frequencies, which is compared with a threshold value of 8 close to zero, the condition is met or not met

вычисляется производная оценки дальности

, вычисляется дальность Д*(k+1) на основе динамической модели радиальных ФСК взаимного перемещения носителя РЛС и ВЦ, вычисляется модуль разности между оценкой производной дальности

и оценкой скорости

, величина которого сравнивается с порогом ε₁,indicates, respectively, the absence or impact of interference that leads away in speed, the distance to the CC is measured, in accordance with the procedure (1a) - (6a), the formation of a range estimate is carried out,

the derivative of the range estimate is calculated

, the range D*(k+1) is calculated based on the dynamic model of the radial FSK of the mutual movement of the carrier of the radar and AT, the modulus of the difference between the estimate of the derivative range is calculated

and speed rating

, the value of which is compared with the threshold ε ₁ ,

- оценка скорости, сформированная на основе измерения скорости Y(k+1) = [V(k+1)]^T и динамической модели радиальных ФСК, вычисляется модуль разности между оценкой дальностью

и вычисленной дальностью Д*(k+1) на основе динамической модели радиальных ФСК, величина которого сравнивается с порогом ε₂,where

- speed estimate formed on the basis of the speed measurement Y(k+1) = [V(k+1)] ^T and the dynamic model of the radial FSK, the modulus of the difference between the range estimate is calculated

and the calculated range D*(k+1) based on the dynamic model of radial FSK, the value of which is compared with the threshold ε ₂ ,

и скорости

формируются в соответствии с процедурой (1а)-(6а) на основе наблюдения Y(k+1) = [Д(k+1), V(k+1)]^T и динамической модели радиальных ФСК, одновременное выполнение условия (8а) и невыполнение условия (10а) свидетельствует о воздействии только уводящей по дальности помехи, в этом случае оценка скорости

формируется в соответствии с процедурой (1а)-(6а) на основе наблюдения Y(k+1)=[V(k+1)] и динамической модели радиальных ФСК, а оценка дальности

вычисляется без учета измерения дальности путем интегрирования оценки скорости

одновременное невыполнение условия (8а) и выполнение условия (10а) свидетельствует о воздействии уводящих по дальности и скорости помех с функционально-связанным законом увода, в этом случае оценки дальности

и скорости

вычисляются в соответствии с процедурой (1а)-(6а) без учета измерений дальности и скорости Y(k+1) = 0 и только на основе динамической модели радиальных ФСК, одновременное невыполнение условий (9а) и (10а) свидетельствует о воздействии уводящих по дальности и скорости помех без функционально-связанного закона увода, в этом случае оценки дальности

и скорости

также вычисляются в соответствии с процедурой (1а)-(6а) без учета измерений дальности и скорости Y(k+1) = 0 и только на основе динамической модели радиальных ФСК, одновременное невыполнение условия (8а) и выполнение условия (10а) свидетельствует о воздействии только уводящей по скорости помехи, в этом случае оценки дальности

и скорости

формируются в соответствии с процедурой (1а)-(6а) на основе измерения только дальности Y(k+1) = [Д(k+1)] и динамической модели радиальных ФСК.Simultaneous fulfillment of conditions (8a) and (10a) indicates the absence of noise that leads away in speed and range; in this case, the range estimates

and speed

are formed in accordance with the procedure (1a)-(6a) based on the observation Y(k+1) = [D(k+1), V(k+1)] ^T and the dynamic model of radial FGCs, the simultaneous fulfillment of condition (8a) and non-fulfillment of condition (10a) indicates the effect of only interference that leads away in range, in this case, the speed estimate

is formed in accordance with the procedure (1a)-(6a) based on the observation Y(k+1)=[V(k+1)] and the dynamic model of radial FSKs, and the range estimate

calculated without taking into account the range measurement by integrating the speed estimate

Simultaneous non-fulfillment of condition (8a) and fulfillment of condition (10a) indicates the impact of interference that leads away in range and speed with a functionally related law of drift, in this case, the range estimates

and speed

calculated in accordance with the procedure (1a)-(6a) without taking into account the measurements of range and velocity Y(k + 1) = 0 and only on the basis of the dynamic model of radial FSK, the simultaneous failure of conditions (9a) and (10a) indicates the impact range and speed of interference without a functionally related drift law, in this case, the range estimates

and speed

are also calculated in accordance with the procedure (1a)-(6a) without taking into account the measurements of range and velocity Y(k+1) = 0 and only on the basis of the dynamic model of radial FSK, the simultaneous failure of condition (8a) and the fulfillment of condition (10a) indicates under the influence of only speed-stealing interference, in this case, the range estimates

and speed

are formed in accordance with the procedure (1a)-(6a) based on measuring only the range Y(k+1) = [D(k+1)] and the dynamic model of the radial FSK.

The disadvantage of this method of tracking the AT is the low reliability of identifying the joint or separate impact of interference that leads away in range and speed or the absence of such an effect and the assessment of the radial FSK of the mutual movement of the AT and the radar carrier under various options for the impact of such interference due to:

1. Assumptions about the linear nature of the dependence of the FGC on time, while in fact the dynamics of the FGC is non-linear.

2. Non-optimality of the FGC estimates determined on its basis, since they are subject to the validity of the hypothesis about the actual variant of the effect of diverting interference, which is of a probabilistic nature, which means that the estimates are conditionally optimal.

3. The absence of the possibility of integrating information from the radar measuring the FGC and the indicator (detector) of the variant of the effect of eavesdropping interference.

4. The inability to take into account a priori data on a change in the variant of the effect of eavesdropping interference.

5. Lack of adaptation of the surveillance system to various options for the effects of eavesdropping interference.

There is a known method of tracking an AT from the class "aircraft with a turbojet engine" under the influence of interference that leads away in range and speed [2], which consists in the fact that the signal reflected from the target is subjected to narrow-band Doppler filtering based on the FFT procedure and converted into an amplitude-frequency spectrum, the components of which are due to signal reflections from the airframe of the accompanied AT and the rotating blades of the LPC impeller of its power plant, the Doppler frequency count corresponding to the maximum amplitude of the spectral component of the signal spectrum, which corresponds to its reflections from the AT airframe, and the Doppler frequency count corresponding to the maximum amplitude of the spectral component are determined of the signal spectrum, located to the right in the Doppler frequency relative to the spectral component of the signal reflected from the airframe of the CC, the selected samples of the Doppler frequencies are fed to the input of the multichannel joint filter of the CC and the first compressor component of the spectrum signal functioning in accordance with the procedure of quasi-optimal joint filtering of phase coordinates and recognition of the state of the Markov structure of a linear stochastic dynamical system

based on a priori data in the form of a mathematical model (MM) of the "VC - radar - indicator" system with a random jump structure (SSS), including models of linear dynamics of radial FGCs of mutual movement of the carrier of the radar and CC

their measurements in the radar

changing the variant of the effect of eavesdropping interference

indicator of the variant of the effect of eavesdropping interference

uncontrolled random disturbances and interference

under initial conditions

where

k - discrete moment of time;

x _k - vector of radial FSK of mutual displacement of the carrier of the radar and CC;

- вариант воздействия уводящих помех (1 - отсутствие помех; 2 - воздействие только уводящей по скорости помехи; 3 - воздействие только уводящей по дальности помехи; 4 - воздействие уводящих как по скорости, так и по дальности помех);

- variant of the effect of escaping interference (1 - no interference; 2 - impact only of interference that is escaping in speed; 3 - effect of only interference that is escaping in range; 4 - effect of interference that is escaping both in speed and in range);

z _k - radar measurement vector;

- выходные показания индикатора варианта воздействия уводящих помех;

- output indications of the indicator of the variant of the effect of diverting interference;

- условные вероятности смены варианта воздействия уводящих помех;

- conditional probabilities of changing the variant of the effect of diverting interference;

- условные вероятности смены показаний индикатора варианта воздействия уводящих помех;

- conditional probabilities of changing the indications of the indicator of the variant of the effect of diverting interference;

- прогнозируемые на один шаг дискретности вперед и апостериорные соответственно вероятности воздействия уводящих помех по s_k+1 варианту, условные математические ожидания ФСК при фиксированном варианте воздействия уводящих помех, условные КМ ошибок оценивания ФСК при фиксированном варианте воздействия уводящих помех;

- predicted one step forward and a posteriori, respectively, the probabilities of the effect of escaping interference for s _k+1 variant, the conditional mathematical expectations of the FGC under a fixed variant of the effect of escaping interference, the conditional KM of the estimation errors of the FGC under a fixed variant of the effect of escaping interference;

- квазиоптимальная по критерию максимума апостериорной вероятности оценка варианта воздействия уводящих помех;

- quasi-optimal according to the criterion of the maximum a posteriori probability estimate of the variant of the effect of diverting interference;

- апостериорное безусловное математическое ожидание ФСК;

- a posteriori unconditional mathematical expectation of FGC;

- апостериорная безусловная КМ ошибок оценивания ФСК;

- a posteriori unconditional KM of FSK estimation errors;

G _k , Q _k - QM, respectively, vectors of excitation noise F _k ξ _k and interference E _k (s _k )ζ _k ;

ξ _k , ζ _k - standard discrete vector white noise;

Θ _k (s _k ) - conditional KM measurement for a fixed variant of the effect of diverting interference;

A _k , F _k - known matrices of coefficients;

C _k (s _k ), E _k (s _k ) - known matrices of deterministic functions from the variant of the influence of diverting interference s _k ;

- обратная матрица по отношению к матрице Θ_k(s_k);

- inverse matrix with respect to the matrix Θ _k (s _k );

T - matrix transposition operation;

detΘ _k (s _k ) - determinant of the matrix Θ _k (s _k );

exp[⋅] - exponential function,

варианта воздействия уводящих помех, определяется оценка

безусловного математического ожидания ФСК, определяется оценка

безусловной КМ ошибок оценивания ФСК, на основе ММ (24а) динамики радиальных ФСК, включающих дальность до цели, планерные и компрессорные составляющие радиальных скоростей и ускорений взаимного перемещения носителя РЛС и ВЦ, в непрерывном времениassessment is determined

variant of the effect of eavesdropping interference, the assessment is determined

unconditional mathematical expectation of FGC, the estimate is determined

unconditional CM of FSK estimation errors, based on MM (24a) dynamics of radial FSK, including the range to the target, glider and compressor components of the radial velocities and accelerations of the relative movement of the carrier of the radar and computer center, in continuous time

where the indices "p" and "k" refer respectively to the glider and the first compressor components of the spectrum reflected from the CC signal;

D(t), V _sbl (t), a _p (t) - radial FSK, respectively, the range, speed and acceleration of approach of the radar carrier with the CC;

V _p (t), V _to (t) - deterministic components of the radial velocities of approach of the radar carrier with the CC;

ΔV _p (t), ΔV _k (t) - fluctuation components of the radial velocities of approach of the radar carrier with the CC;

a _p (t), a _k (t) - fluctuation components of radial accelerations;

α _p , α _to , - the reciprocal of the correlation time of high-speed fluctuations of the mutual movement of the carrier of the radar and CC;

β _p , β _k - squares of natural frequencies of high-speed fluctuations of the mutual movement of the carrier of the radar and CC;

σ _p , σ _to - root-mean-square deviations (RMS) fluctuations in the acceleration of the mutual movement of the carrier of the radar and CC;

n _p (t), n _to (t) - forming normalized white Gaussian noise;

D ₀ , V _p0 , V _k0 , ΔV _p0 , Δ _k0 , and _p0 , and _k0 are the initial values, respectively, of the distance to the CC, the deterministic and fluctuation components of the radial velocities, the fluctuation components of the radial accelerations,

где Δt - период дискретизации, и на основе ММ (25а) измерений в РЛС функционально-связанных координат, представляемой в процедуре (11а)-(23а) матрицами C_k(s_k) и E_k(s_k), размерностями 7×7, ненулевыми элементами которых являются соответственно c₁₁(s_k); c₂₂(s_k); c₃₃(s_k); с₅₅; с₆₆; e₁₁(s_k); e₂₂(s_k); e₃₃(s_k); e₅₅; e_66, при отсутствии помех спрогнозированные на основе априорных данных (30а)-(36а) ФСК корректируются по результатам измерений D(t), V_п(t), ΔV_п(t), V_к(t), ΔV_к(t) и с₁₁(1)=с₁₁, c₂₂(1)=c₂₂, С₃₃(1)=с₃₃; е₁₁(1)=e₁₁, е₂₂(1)=e₂₂, е₃₃(1)=е₃₃, при воздействии только уводящей по скорости помехи корректируются по результатам измерений D(t),

,

, V_к(t), ΔV_к(t) и с₁₁(2)=с₁₁,

; е₁₁(2)=е₁₁,

, при воздействии только уводящей по дальности помехи корректируются по результатам измерений D*(t), V_n(t), ΔV_n(t), V_к(t), ΔV_к(t) и

, c₂₂(3)=c₂₂, с₃₃(3)=с₃₃;

, e₂₂(3)=e₂₂, е₃₃(3)=е₃₃, при воздействии уводящих как по скорости, так и по дальности помех корректируются по результатам измерений D*(t),

,

, V_к(t), ΔV_к(t) и

,

,

;

,

,

, где символом «*» отмечены компоненты вектора ФСК, на искажение которых направлено воздействие уводящих помех, а также измененные элементы матриц C_k(s_k) и E_k(s_k), компенсирующие в РЛС соответствующие воздействия.represented in the procedure (11a)-(23a) by matrices A _k and F _k , dimensions 7×7, non-zero elements of which are respectively a ₁₁ = a ₂₂ = a ₃₃ = a ₅₅ = a ₆₆ =1; a ₁₂ \u003d a ₁₃ \u003d -Δt; a ₃₄ = a ₆₇ =Δt; a ₄₄ \ _u003d 1- a nΔ t; a ₇₇ \u003d 1- a _to Δt; a ₄₃ \u003d -βpΔt; a ₇₆ =-β _to Δt;

where Δt is the sampling period, and based on the MM (25a) measurements in the radar of functionally related coordinates, represented in the procedure (11a)-(23a) by the matrices C _k (s _k ) and E _k (s _k ), dimensions 7×7 , whose nonzero elements are respectively c ₁₁ (s _k ); c ₂₂ (s _k ); c ₃₃ (s _k ); from ₅₅ ; from ₆₆ ; e ₁₁ (s _k ); e ₂₂ (s _k ); e ₃₃ (s _k ); e ₅₅ ; e _66, in the absence of interference predicted on the basis of a priori data (30a)-(36a) FSK are corrected according to the measurement results D(t), V _p (t), ΔV _p (t), V _k (t), ΔV _k (t ) and c ₁₁ (1)=c ₁₁ , c ₂₂ (1)=c ₂₂ , C ₃₃ (1)=c ₃₃ ; e ₁₁ (1) = e ₁₁ , e ₂₂ (1) = e ₂₂ , e ₃₃ (1) = e ₃₃

,

, V _to (t), ΔV _to (t) and s ₁₁ (2)=s ₁₁ ,

; e ₁₁ (2) \u003d e ₁₁ ,

, when exposed to only distance-leading interference, they are corrected according to the measurement results D * (t), V _n (t), ΔV _n (t), V _k (t), ΔV _k (t) and

, c ₂₂ (3)=c ₂₂ , c ₃₃ (3)=c ₃₃ ;

, e ₂₂ (3)=e ₂₂ , e ₃₃ (3)=e ₃₃ , under the influence of noise that leads both in speed and in range, they are corrected according to the results of measurements D*(t),

,

, V _to (t), ΔV _to (t) and

,

,

;

,

,

, where the symbol "*" marks the components of the FSK vector, the distortion of which is directed by the effect of escaping interference, as well as the changed elements of the matrices C _k (s _k ) and E _k (s _k ), compensating the corresponding effects in the radar.

In FIG. Figure 1 shows a block diagram explaining the implementation of a known method of tracking an AT from the class "aircraft with turbojet engines" under the influence of interference that leads away in range and speed [2].

The disadvantage of this method of tracking the AT is the low reliability of identifying the joint or separate impact of interference that leads away in range and speed or the absence of such an effect and the assessment of the radial FSK of the mutual movement of the AT and the radar carrier under various options for the impact of such interference due to:

1. Assumptions about the linear nature of the dependence of the FGC on time, while in fact the dynamics of the FGC is non-linear.

2. Assumptions about the statistical independence of the change in the options for the impact of escaping interference from the FGC, while in fact the probabilities of changing such options depend on the phase coordinates, in particular, with a decrease in the distance to the target, the probabilities of transitions to the variant of the combined effect of escaping interference in range and speed increase.

3. Assumptions about the normality of the approximating conditional probability density of the FSK under a fixed variant of the effect of diverting interference - a significant difference in the form of the actual probability density of the FSK from the normal form of the approximating density leads to an increase in estimation errors.

The purpose of the invention is to increase the reliability of identifying the joint or separate impact of interference that leads away in range and speed or the absence of their impact and estimating the radial functionally related range to the CC and the speed of approach of the radar carrier with it by adaptive two-time parametric approximation of unknown probability densities of the FSK with a mixture of a priori specified approximating functions and approximation of the resulting estimates to their optimal values by taking into account nonlinearities in the dynamics of the FGC and their measurements, taking into account the statistical dependence of the probabilities of changing options for the effects of fading interference from the FSK, integrating the information of the radar and the indicator of the variant of the effect of fading interference, taking into account a priori data on the change of these options and adaptation surveillance systems for them.

To achieve the goal in the method of tracking an AT from the class "aircraft with a turbojet engine" under the influence of interference that leads away in range and speed [2], which consists in the fact that the signal reflected from the target is subjected to narrow-band Doppler filtering based on the FFT procedure and converted into amplitude- the frequency spectrum, the components of which are due to signal reflections from the airframe of the accompanied AT and the rotating blades of the LPC impeller of its power plant, the Doppler frequency reading corresponding to the maximum amplitude of the spectral component of the signal spectrum, which corresponds to its reflections from the AT airframe, and the Doppler frequency reading corresponding to the maximum amplitude of the spectral component of the signal spectrum, which is located to the right in the Doppler frequency relative to the spectral component of the signal reflected from the airframe of the computer center, the selected samples of the Doppler frequencies are additionally fed to the input of the multichannel joint filter of the computer center and the first compressor conflicting component of the signal spectrum and identification of the variant of the effect of diverting interference, functioning in accordance with the procedure of quasi-optimal joint filtering of phase coordinates and recognition of the state of the conditionally Markov structure of a nonlinear stochastic dynamic system during observation without delay [3] in accordance with functional integral recurrent equations

which, after performing the approximation procedure (putting forward a hypothesis regarding the types of approximating functions) in accordance with the expressions

are closed (the number of unknowns becomes equal to the number of equations), the integrals on the right-hand sides of the equations are expressed in terms of elementary or tabulated functions, and the equations themselves degenerate into the following ordinary recursive equations with respect to the conditional probabilities of the influence of diverting noise in various options (states of the structure) with a fixed set of approximating functions, conditional MO of functionally-related coordinates and KM of their estimation errors for a fixed variant of the set of approximating functions and the variant of the influence of diverting noise:

based on a priori data in the form of the MM of the system "VC - radar - indicator" with CCC, including, in general terms, a nonlinear model of the dynamics of radial FSK - range to the target, glider and compressor components of radial velocities and accelerations of the mutual movement of the carrier of the radar and AT

nonlinear model of measurements of these FSK in the radar

conditional-Markov model of changing the variant of the influence of diverting interference

conditional Markov model of the indicator of the variant of the effect of eavesdropping interference

model of uncontrolled random disturbances and interference

under initial conditions

where

n = (n ₁ , n ₂ , n ₃ , n ₄ , n ₅ ) - vector of ordinal numbers of types of approximating functions, determines the variant of the set of approximating functions;

- порядковый номер функции, аппроксимирующей модель динамики ФСК, из конечного множества таких функций

;

- the ordinal number of the function approximating the FGC dynamics model from a finite set of such functions

;

- порядковый номер функции, аппроксимирующей модель измерения ФСК, из конечного множества таких функций

;

- serial number of the function approximating the FSK measurement model from a finite set of such functions

;

- порядковый номер функции, аппроксимирующей зависимость вероятностей смены вариантов воздействия уводящих помех от значений ФСК, из конечного множества таких функций

;

- the ordinal number of the function approximating the dependence of the probabilities of changing the options for the effect of eavesdropping interference on the values of the FSK, from a finite set of such functions

;

- порядковый номер функции, аппроксимирующей зависимость вероятностей смены показаний индикатора варианта воздействия уводящих помех от значений ФСК, из конечного множества таких функций

;

- the ordinal number of the function approximating the dependence of the probability of changing the indications of the indicator of the variant of the effect of diverting interference on the values of the FGC, from a finite set of such functions

;

- порядковый номер вида аппроксимирующей условной плотности вероятности

ФСК при фиксированном варианте воздействия уводящих помех, из априорно задаваемого конечного множества

таких функций;

- ordinal number of the type of approximating conditional probability density

FSK under a fixed variant of the effect of diverting interference, from an a priori specified finite set

such functions;

N is the number of alternative sets of types of approximating functions;

N ₁ , N ₂ , N ₃ , N ₄ and N ₅ - the number of elements of the sets respectively Φ, Ψ, Θ, P and F;

k - discrete moment of time;

x _k = (D, V _{n, k,} ΔV _{n, k,} and _{n, k,} V _{a, k,} ΔV _{to, k,} and _{a, k)} ^T - vector radial FSK comprising radial distance to the VTS, glider and compressor components of the radial velocity and acceleration of the relative movement of the radar carrier and the target;

- номер варианта воздействия уводящих помех (1 - отсутствие помех; 2 - воздействие только уводящей по скорости помехи; 3 - воздействие только уводящей по дальности помехи; 4 - воздействие уводящих как по скорости, так и по дальности помех);

- the number of the variant of the influence of the distracting interference (1 - the absence of interference; 2 - the impact of only the interference, which is distracting in speed; 3 - the impact of the interference, which is distracting in terms of range; 4 - the impact of the interference, which is distracting both in speed and in range);

- вектор измерений в РЛС функционально-связанных координат;

- vector of measurements in the radar of functionally related coordinates;

- выходные показания индикатора (обнаружителя) варианта воздействия уводящих помех;

- output indications of the indicator (detector) of the variant of the effect of eavesdropping interference;

ξ _k , ζ _k - vectors, respectively, of random perturbations affecting the CC, and interference, affecting the radar;

ϕ(⋅) and ψ(⋅) are known, in general form, non-linear deterministic vector functions of random arguments;

- известные условные вероятности смены вариантов воздействия уводящих помех;

- known conditional probabilities of changing the options for the effect of eavesdropping interference;

- известные условные вероятности смены показаний индикатора варианта воздействия уводящих помех;

- known conditional probabilities of changing the indications of the indicator of the variant of the effect of diverting interference;

Φ(ξ _k , ζ _k ) - joint distribution function of disturbances and noise;

- условная функция распределения помех при фиксированных возмущениях;

- conditional distribution function of interference for fixed disturbances;

Φ(ξ _k ) - perturbation distribution function;

ƒ(x_k, s_k) is the joint probability density of the FSK and the variant of the effect of eavesdropping interference;

- условная плотность вероятности ФСК при фиксированном варианте воздействия уводящих помех;

- conditional probability density of the FSK for a fixed variant of the effect of diverting interference;

- условная плотность вероятности ФСК при фиксированном варианте воздействия уводящих помех и фиксированном варианте набора аппроксимирующих функций;

- conditional probability density of the FSK under a fixed variant of the effect of diverting interference and a fixed variant of the set of approximating functions;

- прогнозируемая на один шаг дискретности вперед условная плотность вероятности ФСК при фиксированном варианте воздействия уводящих помех и фиксированном варианте набора аппроксимирующих функций;

- the conditional probability density of the FSK predicted one discrete step ahead for a fixed variant of the effect of diverting noise and a fixed variant of the set of approximating functions;

- апостериорная условная плотность вероятности ФСК при фиксированном варианте воздействия уводящих помех и фиксированном варианте набора аппроксимирующих функций;

- a posteriori conditional probability density of the FSK for a fixed variant of the influence of diverting noise and a fixed variant of the set of approximating functions;

- n₅-й ВИД функции, аппроксимирующей условную плотность вероятности ФСК при фиксированном варианте воздействия уводящих помех;

- n ₅ th VIEW of the function approximating the conditional probability density of the FGC for a fixed variant of the effect of diverting interference;

- n₅-й вид функции, аппроксимирующей прогнозируемую на один шаг дискретности вперед условную плотность вероятности ФСК при фиксированном варианте воздействия уводящих помех;

- n _5th type of function approximating the conditional probability density of the FGC predicted one step ahead of the discreteness for a fixed variant of the effect of escaping interference;

- n₅-й вид функции, аппроксимирующей апостериорную условную плотность вероятности фазовых координат ФСК при фиксированном варианте воздействия уводящих помех;

- n _5th type of function approximating the a posteriori conditional probability density of the phase coordinates of the FGC for a fixed variant of the effect of diverting interference;

- прогнозируемые на один шаг дискретности вперед и апостериорные соответственно вероятности воздействия уводящих помех по s_k+1-му варианту при фиксированном n-м варианте набора аппроксимирующих функций, условные МО функционально-связанных координат при фиксированном варианте воздействия уводящих помех и фиксированном n-м варианте набора аппроксимирующих функций, условные КМ ошибок оценивания ФСК при фиксированном варианте воздействия уводящих помех и фиксированном n-м варианте набора аппроксимирующих функций;

- predicted one step forward and a posteriori, respectively, the probabilities of the effect of escaping interference according to the s _{k + 1} -th variant with a fixed n-th variant of the set of approximating functions, conditional MO of functionally related coordinates with a fixed variant of the influence of escaping interference and a fixed n-th variant a set of approximating functions, conditional KM of errors in estimating the FSK under a fixed variant of the effect of diverting noise and a fixed n-th variant of a set of approximating functions;

- начальные условия;

- initial conditions;

^_ условные плотности вероятности соответственно ФСК и их измерений в РЛС при фиксированных {s_k+1, x_k, s_k} и {х_k, s_k, r_k};

^_ conditional probability densities, respectively, of the FSK and their measurements in the radar at fixed {s _k+1 , x _k , s _k } and {х _k , s _k , r _k };

n _x , n _z are the dimensions of the FGC vectors and their measurements, respectively;

- нормировочный коэффициент при фиксированном варианте набора аппроксимирующих функций;

- normalization coefficient for a fixed set of approximating functions;

- апостериорные условные квазиоптимальные оценки соответственно варианта воздействия уводящих помех (по критерию максимума апостериорной вероятности), математического ожидания ФСК и КМ ошибок их оценивания при фиксированном варианте набора аппроксимирующих функций;

- a posteriori conditional quasi-optimal estimates, respectively, of the variant of the effect of diverting interference (according to the criterion of the maximum a posteriori probability), the mathematical expectation of the FSK and the CM of their estimation errors for a fixed version of the set of approximating functions;

- апостериорная вероятность соответствия варианта набора аппроксимирующих функций фактическому виду закономерностей взаимного перемещения носителя РЛС и ВЦ, воздействия со стороны цели на РЛС помех, измерения в радиолокационной станции ФСК и идентификации в индикаторе помеховой обстановки варианта воздействия уводящих помех (далее фактическому виду закономерностей взаимного перемещения носителя РЛС и ВЦ);

- a posteriori probability of the correspondence of the variant of the set of approximating functions to the actual form of the patterns of mutual movement of the radar carrier and the CC, the impact of interference from the target on the radar, measurements in the FSK radar station and identification in the indicator of the interference situation of the variant of the effect of escaping interference (hereinafter, the actual form of the patterns of mutual movement of the radar carrier and VC);

- квазиоптимальная по критерию максимума апостериорной вероятности идентификация моделей соответственно динамики ФСК

, их измерений

, смены варианта воздействия уводящих помех

, индикатора (обнаружителя) варианта воздействия уводящих помех

и условной плотности вероятности фазовых координат при фиксированном варианте воздействия уводящих помех

, из вариантов набора аппроксимирующих функций задаваемых множествами Φ, Ψ, Θ, Р и F;

- quasi-optimal according to the criterion of maximum a posteriori probability identification of models according to the dynamics of the FGC

, their measurements

, changing the variant of the effect of eavesdropping interference

, indicator (detector) of the variant of the effect of eavesdropping

and the conditional probability density of phase coordinates for a fixed variant of the influence of diverting interference

, from the variants of the set of approximating functions given by the sets Φ, Ψ, Θ, Р and F;

- квазиоптимальная по критерию максимума апостериорной вероятности оценка условной плотности вероятности ФСК при фиксированном варианте воздействия уводящих помех смесью аппроксимирующих функций из множества F;

- quasi-optimal according to the criterion of the maximum a posteriori probability estimate of the conditional probability density of the FSK for a fixed variant of the influence of diverting noise by a mixture of approximating functions from the set F;

- апостериорные условные квазиоптимальные оценки соответственно варианта воздействия уводящих помех (по критерию максимума апостериорной вероятности), математического ожидания ФСК и КМ ошибок их оценивания при квазиоптимальном наборе аппроксимирующих смесей

;

- a posteriori conditional quasi-optimal estimates, respectively, of the variant of the effect of diverting noise (according to the criterion of the maximum a posteriori probability), the mathematical expectation of the FSK and the CM of their estimation errors with a quasi-optimal set of approximating mixtures

;

T - matrix transposition operation;

exp{⋅} - exponential function;

i - imaginary unit;

ω - frequency;

G: - statistical hypothesis, which consists in the fact that ...;

,

таких, что … (по аналогии в (31), (34), (36));ϕ(s _k+1 , x _k , s _k , ξ _k ) → Φ: - in (28), choice for a given function ϕ(s _k+1 , x _k , s _k , ξ _k ) of the set Φ of types of approximating functions

,

such that ... (by analogy in (31), (34), (36));

- n₁-й вид аппроксимирующей функции из множества Φ таких функций (по аналогии для функций ψ_n2 (⋅), q_n3 (⋅), π_n4 (⋅), f_n5 (⋅) из множеств Ψ, Θ, Р, F);

- n _1st type of approximating function from the set Φ of such functions (by analogy for the functions ψ _n2 (⋅), q _n3 (⋅), π _n4 (⋅), f _n5 (⋅) from the sets Ψ, Θ, Р, F );

- функция, состоящая только из элементарных или табулированных функций (по аналогии для функций

);

- a function consisting only of elementary or tabulated functions (by analogy for functions

);

и

- n₁-й и n₂-й виды функций, аппроксимирующих условные плотности вероятности соответственно ФСК и их измерений при фиксированных {s_k+1, x_k, s_k}, и {x_k, s_k, r_k},

and

- n ₁ -th and n ₂ -th types of functions approximating the conditional probability densities, respectively, of the FGC and their measurements for fixed {s _k+1 , x _k , s _k }, and {x _k , s _k , r _k },

- квантор всеобщности [(

а,b)с - для любых а и b выполняется с];

- universal quantifier [(

a, b) c - for any a and b, c] is performed;

,

→ F - choice of the set F of types of approximating functions

,

и

- условные соответственно МО функционально-связанных координат и КМ (для одномерного случая - дисперсия) ошибок их оценивания при фиксированной варианте воздействия уводящих помех s_k;

and

- conditional, respectively, MO of functionally-related coordinates and QM (for the one-dimensional case - dispersion) of their estimation errors for a fixed variant of the effect of escaping interference s _k ;

{Φ, Ψ, Θ, P, F}: - set of sets of types of approximating functions such that …;

- функция правдоподобия;

- likelihood function;

- идентификация квазиоптимального вида аппроксимирующей функции модели динамики ФСК ϕ(s_k+1, х_k, s_k, ξ_k) по его порядковому номеру n₁ в множестве Φ видов таких функций (по аналогии для функций ϕ(⋅), q(⋅), π(⋅), ƒ(⋅) в множествах Ψ, Θ, Р, F);

- identification of the quasi-optimal form of the approximating function of the FGC dynamics model ϕ(s _k+1 , x _k , s _k , ξ _k ) by its ordinal number n ₁ in the set Φ of the types of such functions (by analogy for the functions ϕ(⋅), q(⋅ ), π(⋅), ƒ(⋅) in the sets Ψ, Θ, Р, F);

- квазиоптимальная по критерию максимума апостериорной вероятности оценка модели динамики ФСК смесью аппроксимирующих функций из множества Φ;

- quasi-optimal according to the criterion of the maximum a posteriori probability estimate of the FGC dynamics model by a mixture of approximating functions from the set Φ;

- квазиоптимальная по критерию максимума апостериорной вероятности оценка модели измерения ФСК, смесью аппроксимирующих функций из множества Ψ;

- quasi-optimal according to the criterion of the maximum a posteriori probability estimate of the FSK measurement model, by a mixture of approximating functions from the set Ψ;

- квазиоптимальная по критерию максимума апостериорной вероятности оценка модели смены варианта воздействия уводящих помех, смесью аппроксимирующих функций из множества Θ;

- quasi-optimal according to the criterion of the maximum a posteriori probability estimate of the model for changing the variant of the effect of diverting interference, by a mixture of approximating functions from the set Θ;

- квазиоптимальная по критерию максимума апостериорной вероятности оценка модели индикатора варианта воздействия уводящих помех, смесью аппроксимирующих функций из множества Р;

- quasi-optimal according to the criterion of the maximum a posteriori probability estimate of the model of the indicator of the variant of the effect of diverting interference, by a mixture of approximating functions from the set P;

- квазиоптимальная по критерию максимума апостериорной вероятности оценка набора моделей соответственно динамики ФСК

, их измерений

, смены варианта воздействия уводящих помех

, индикатора варианта воздействия уводящих помех

и условной плотности вероятности ФСК при фиксированном варианте воздействия уводящих помех

, смесью априорно выбираемых аппроксимирующих функций из множеств Φ, Ψ, Θ, Р и F;

- quasi-optimal according to the criterion of the maximum a posteriori probability estimate of the set of models according to the dynamics of the FGC

, their measurements

, changing the variant of the effect of eavesdropping interference

, indicator of the variant of the effect of eavesdropping interference

and the conditional probability density of the FSK for a fixed variant of the effect of eavesdropping interference

, a mixture of a priori chosen approximating functions from the sets Φ, Ψ, Θ, Р and F;

- апостериорные условные квазиоптимальные оценки соответственно варианта воздействия уводящих помех (по критерию максимума апостериорной вероятности), МО функционально-связанных координат и КМ ошибок их оценивания при квазиоптимальном наборе аппроксимирующих смесей

;

- a posteriori conditional quasi-optimal estimates, respectively, of the variant of the effect of diverting interference (according to the criterion of the maximum a posteriori probability), the MO of functionally related coordinates and the CM of their estimation errors with a quasi-optimal set of approximating mixtures

;

n ^(s) - power (number of elements) of the set of options for the effect of diverting interference;

x _min (s ₀ ) and x _max (s ₀ ) are the vectors of the minimum and maximum values of the FGC, respectively, for a fixed variant of the effect of diverting interference at the initial moment of time;

x _{min i} (s ₀ ) and x _{max i} (s ₀ ) - ie components of the vectors of the minimum and maximum values of the FGC, respectively, under a fixed variant of the effect of escaping interference at the initial moment of time,

варианта воздействия уводящих помех при оптимальном наборе аппроксимирующих смесей из априорно выбираемого множества функций, определяется оценка

безусловного по отношению к вариантам воздействия уводящих помех математического ожидания ФСК при оптимальном наборе аппроксимирующих смесей, определяется оценка

безусловной по отношению к вариантам воздействия уводящих помех ковариационной матрицы ошибок оценивания фазовых координат при оптимальном наборе аппроксимирующих смесей, на основе ММ (69)-(74) системы «ВЦ - РЛС - индикатор» со ССС, включающей, в общем виде, нелинейные и условно-марковские модели.assessment is determined

of the variant of the influence of diverting noises with an optimal set of approximating mixtures from an a priori chosen set of functions, the estimate is determined

unconditional with respect to the variants of the influence of the distracting interference of the mathematical expectation of the FGC with an optimal set of approximating mixtures, the estimate is determined

unconditional with respect to the options for the effects of diverting interference of the covariance matrix of errors in estimating phase coordinates with an optimal set of approximating mixtures, based on MM (69) - (74) of the "CC - radar - indicator" system with CCC, including, in general terms, nonlinear and conditionally -Markov models.

At the same time, Pearson's four-parameter distributions are proposed as approximating distributions when any two of its parameters are known (specified) [its special cases: Gaussian, truncated Gaussian, beta distribution (and its special cases: arcsine law, uniform and power distributions) , gamma distribution (and its special cases: exponential and exponential-power distributions, χ ² - distribution, Erlang's law), Student's T-distribution], as well as such two-parameter distributions as Simpson's law, Rayleigh, Maxwell's, Pareto's, logistic distribution and F-distribution of Fisher [3].

New features with significant differences are:

1. The use of a multi-channel filter, both in terms of the number of options for the effect of distracting interference, and in the number of options for a set of approximating functions, the filter for joint estimation of the radial distance to the target, the airframe and the first compressor components of the radial speed and the acceleration of the mutual movement of the radar carrier and the target, and recognition of the effect option diverting noise, functioning in accordance with the procedure (1)-(74) of quasi-optimal joint filtering of phase coordinates and recognition of the state of the conditionally Markov structure of a nonlinear stochastic dynamic system during observation without delay, instead of a single-channel, according to the number of options for a set of approximating functions, filter, functioning in accordance with with the procedure of multidimensional linear discrete Kalman filtering [1], and instead of a single-channel filter, according to the number of options for a set of approximating functions, that operates in accordance with the procedure of quasi-optimal joint filtering of phase coordinates and p recognition of the state of the Markov structure of a linear stochastic dynamical system during observation without delay based on a two-time parametric approximation by a normal distribution law [2, 3].

2. Automatic selection (51)-(56) of a set of types of approximating functions from a priori specified sets (28), (31), (34), (36), (38) of such functions directly in the process of filter operation.

3. Automatic formation (57)-(61) of a set of mixtures of approximating functions from a priori specified sets of such functions directly in the process of filter operation.

,

,

,

и

в (41)-(49), на основе априорных данных о смене варианта воздействия уводящих помех и динамике ФСК, представленных соответственно начальными (74), (66) и переходными (71) вероятностями условной цепи Маркова и моделью (69), по результатам измерений в (19), (32), (44)-(46), (50) и показаниям индикатора варианта воздействия уводящих помех в (18), (36), (44)-(46), (50) с альтернативными моделями измерений (70), соответствующими различным вариантам воздействия уводящих помех, и моделью индикатора (72).4. Joint estimation of the FSK (42), (43), (45), (46), (48), (49), (63), (64) and recognition of the variant of the effect of stealth interference (41), (44), (47), (62) based on a two-time parametric approximation [3] in N multichannel quasi-optimal filters in terms of the number of options for the effect of diverting interference, differing in the set of types of approximating functions

,

,

,

and

in (41)-(49), on the basis of a priori data on the change in the variant of the effect of diverting interference and the dynamics of the FGC, represented respectively by the initial (74), (66) and transition (71) probabilities of the conditional Markov chain and the model (69), according to the results measurements in (19), (32), (44)-(46), (50) and indications of the indicator of the variant of the effect of eavesdropping interference in (18), (36), (44)-(46), (50) with alternative measurement models (70) corresponding to different options for the effect of eavesdropping interference, and an indicator model (72).

5. Combination of radar measurements with model (70) and indications of the indicator of the variant of the effect of eavesdropping interference with model (72).

6. Adaptation of the filter to various variants of the effect of stole interference with simultaneous refinement of the mathematical models used.

воздействия уводящих помех по каждому варианту на один шаг дискретности вперед в каждом фильтре при фиксированном варианте набора аппроксимирующих функций, на основе априорных данных о смене варианта воздействия уводящих помех, представленных соответственно начальными (74), (66) и переходными (71) вероятностями условной цепи Маркова.7. Forecasting (41) probabilities

effects of escaping interference for each variant by one discrete step forward in each filter with a fixed variant of the set of approximating functions, based on a priori data on the change in the variant of the effect of escaping interference, represented respectively by the initial (74), (66) and transient (71) probabilities of the conditional chain Markov.

ФСК на один шаг дискретности вперед в каждом фильтре при фиксированных варианте набора аппроксимирующих функций и варианте воздействия уводящих помех, с учетом найденных вероятностей (41) на основе априорных данных о смене этих вариантов (71) и динамике ФСК взаимного перемещения носителя РЛС и ВЦ (69), с учетом найденной, как обратное преобразование Фурье от характеристической функции ФСК, в (20), (29) условной плотности вероятности

и ее аппроксимирующей функции

8. Forecasting (42) Conditional Mathematical Expectations

FSK one discrete step forward in each filter for a fixed variant of the set of approximating functions and the variant of the effect of diverting interference, taking into account the found probabilities (41) based on a priori data on the change of these options (71) and the dynamics of the FSK of the relative movement of the carrier of the radar and CC (69 ), taking into account the conditional probability density found in (20), (29) as the inverse Fourier transform of the FSK characteristic function

and its approximating function

ошибок оценивания ФСК на один шаг дискретности вперед в каждом фильтре при фиксированных варианте набора аппроксимирующих функций и варианте воздействия уводящих помех, с учетом найденных вероятностей (41) и математических ожиданий (42).9. Forecasting (43) conditional CM

FSK estimation errors by one discrete step forward in each filter for a fixed variant of the set of approximating functions and the variant of the effect of diverting noise, taking into account the found probabilities (41) and mathematical expectations (42).

воздействия уводящих помех по каждому варианту, в каждом фильтре при фиксированном варианте набора аппроксимирующих функций, по степени согласованности, представленной функцией правдоподобия, спрогнозированных вероятностей (41), математических ожиданий (42) ФСК и КМ (43) ошибок их оценивания с результатами измерений в (19), (32), (44)-(46), (50) и показаниями индикатора в (18), (36), (44)-(46), (50), с учетом найденной, как обратное преобразование Фурье от характеристической функции измерений, в (19), (32) условной плотности вероятности

и ее аппроксимирующей функции

10. Estimation (44) of a posteriori probabilities

effects of diverting interference for each option, in each filter with a fixed variant of the set of approximating functions, according to the degree of consistency represented by the likelihood function, predicted probabilities (41), mathematical expectations (42) FSK and CM (43) errors of their estimation with the measurement results in ( 19), (32), (44)-(46), (50) and the indicator readings in (18), (36), (44)-(46), (50), taking into account the found one, as the inverse Fourier transform on the characteristic function of measurements, in (19), (32) the conditional probability density

and its approximating function

ФСК взаимного перемещения носителя РЛС и ВЦ в каждом фильтре при фиксированном варианте набора аппроксимирующих функций, для каждой альтернативной модели измерения (70), соответствующей различным вариантам воздействия уводящих помех, на основе спрогнозированных математических ожиданий (42) и КМ (43) ошибок прогноза с учетом результатов измерения в (19), (32), (44)-(46), (50) и показаний индикатора в (18), (36), (44)-(46), (50).11. Estimation (45) of conditional a posteriori mathematical expectations

FSK of mutual movement of the carrier of the radar and AT in each filter with a fixed variant of the set of approximating functions, for each alternative measurement model (70) corresponding to different options for the effect of diverting interference, based on the predicted mathematical expectations (42) and KM (43) of forecast errors, taking into account measurement results in (19), (32), (44)-(46), (50) and indicator readings in (18), (36), (44)-(46), (50).

ошибок фильтрации ФСК в каждом фильтре при фиксированном варианте набора аппроксимирующих функций, для каждой альтернативной модели измерения (70), соответствующей различным вариантам воздействия уводящих помех, на основе спрогнозированных математических ожиданий (42) и КМ (43) ошибок прогноза с учетом результатов измерения в (19), (32), (44)-(46), (50) и показаний индикатора в (18), (36), (44)-(46), (50).12. Estimation (46) of conditional a posteriori QM

FSK filtering errors in each filter with a fixed variant of the set of approximating functions, for each alternative measurement model (70) corresponding to different options for the effect of diverting interference, based on the predicted mathematical expectations (42) and KM (43) of the prediction errors, taking into account the measurement results in ( 19), (32), (44)-(46), (50) and indicator readings in (18), (36), (44)-(46), (50).

варианта воздействия уводящих помех в каждом фильтре при фиксированном варианте набора аппроксимирующих функций, для которого найденная апостериорная вероятность (44) окажется больше.13. Identification (47) of such

of the variant of the influence of diverting noise in each filter for a fixed variant of the set of approximating functions, for which the found a posteriori probability (44) turns out to be greater.

в каждом фильтре при фиксированном варианте набора аппроксимирующих функций на основе апостериорных вероятностей (44) воздействия уводящих помех по каждому варианту и условных апостериорных оценок (45) ФСК, как безусловного математического ожидания.14. Finding (48) unconditional, in relation to the options for the impact of eavesdropping interference, an assessment of the FGC

in each filter with a fixed variant of a set of approximating functions based on a posteriori probabilities (44) of the effect of escaping interference for each variant and conditional a posteriori estimates (45) of the FSK as an unconditional mathematical expectation.

ошибок оценивания ФСК в каждом фильтре при фиксированном варианте набора аппроксимирующих функций с учетом найденных апостериорных вероятностей (44) воздействия уводящих помех по каждому варианту, условных математических ожиданий ФСК (45), условных КМ (46) ошибок их оценивания и безусловных оценок ФСК (48).15. Finding (49) unconditional in relation to the options for the impact of spoofing noise KM

FSK estimation errors in each filter for a fixed variant of the set of approximating functions, taking into account the found a posteriori probabilities (44) of the effect of diverting noise for each option, conditional mathematical expectations of the FSK (45), conditional KM (46) of their estimation errors and unconditional estimates of the FSK (48) .

соответствия наборов видов аппроксимирующих функций из задаваемых множеств таких функций фактическому виду закономерностей взаимного перемещения носителя РЛС и ВЦ, для каждого фильтра на (k+1) -м шаге дискретности, по степени согласованности, представленной функцией правдоподобия, спрогнозированных вероятностей (41), математических ожиданий (42) ФСК и КМ (43) ошибок их оценивания с результатами очередных измерений в (19), (32), (44)-(46), (50) и показаний индикатора в (18), (36), (44)-(46), (50), с учетом найденной, как обратное преобразование Фурье от характеристической функции измерений, в (19), (31) условной плотности вероятности

и ее аппроксимирующей функции

16. Correction (50) of a posteriori probabilities

correspondence of sets of types of approximating functions from given sets of such functions to the actual form of patterns of mutual movement of the carrier of the radar and AT, for each filter at the (k + 1) -th step of discreteness, according to the degree of consistency represented by the likelihood function, predicted probabilities (41), mathematical expectations (42) FSK and CM (43) errors in their estimation with the results of regular measurements in (19), (32), (44)-(46), (50) and indicator readings in (18), (36), (44 )-(46), (50), taking into account the conditional probability density found in (19), (31) as the inverse Fourier transform of the characteristic measurement function

and its approximating function

из их множеств Φ, Ψ, Θ, Р и F, для которого найденная вероятность (50) окажется больше.17. Identification (51)-(56) of such a variant of a set of approximating functions (models)

from their sets Φ, Ψ, Θ, Р and F, for which the found probability (50) turns out to be greater.

, набором

смесей аппроксимирующих функций из априорно задаваемых множеств Φ, Ψ, Θ, Р и F, взятых с весовыми коэффициентами, пропорциональными вероятностям

соответствия видов этих функций фактическому виду закономерностей взаимного перемещения носителя РЛС и ВЦ.18. Estimation (57)-(61) of a set of models, respectively, of the dynamics of the FSK ϕ(⋅) of their measurements in the radar ψ(⋅), the change in the variant of the effect of escaping interference q(⋅), the indicator of the effect of escaping interference, and the conditional probability density of the FSK with a fixed variant interference interference

, set

mixtures of approximating functions from a priori given sets Φ, Ψ, Θ, Р and F, taken with weight coefficients proportional to the probabilities

the correspondence of the types of these functions to the actual form of the patterns of mutual movement of the carrier of the radar and CC.

воздействия уводящих помех с учетом оценок вероятностей (50) соответствия наборов видов аппроксимирующих функций фактическому виду закономерностей взаимного перемещения носителя РЛС и ВЦ, и апостериорных условных вероятностей (44) воздействия уводящих помех по каждому варианту при фиксированном варианте набора аппроксимирующих функций.19. Identification (62) variant

the effects of escaping interference, taking into account the estimates of the probabilities (50) of the correspondence of sets of types of approximating functions to the actual form of the patterns of mutual movement of the carrier of the radar and CC, and a posteriori conditional probabilities (44) of the effects of escaping interference for each variant with a fixed variant of the set of approximating functions.

с учетом найденных условных оценок функционально-связанных координат (48) при фиксированном варианте набора аппроксимирующих функций и вероятностей (44), как безусловного, по отношению к вариантам набора аппроксимирующих функций, математического ожидания.20. Estimation (63) FSK

taking into account the found conditional estimates of functionally related coordinates (48) with a fixed version of the set of approximating functions and probabilities (44), as an unconditional, in relation to the variants of the set of approximating functions, mathematical expectation.

ошибок оценивания ФСК с учетом найденных апостериорных вероятностей (50) соответствия вариантов набора аппроксимирующих функций фактическим видам закономерностей, условных математических ожиданий ФСК (48) и КМ (49) ошибок их оценивания при фиксированном варианте набора аппроксимирующих функций, и безусловных оценок ФСК (63).21. Estimation (64) of the unconditional with respect to variants set of approximating functions of QM

FSK estimation errors, taking into account the found a posteriori probabilities (50), correspondence of variants of the set of approximating functions to the actual types of regularities, conditional mathematical expectations of FSK (48) and QM (49), errors in their estimation with a fixed version of the set of approximating functions, and unconditional estimates of FSK (63).

22. Acceptance of equiprobable (66) and uniform (67), (68), initial conditions (74), in the absence of additional a priori data, respectively, for the variant of the effect of eavesdropping interference and FSK of the mutual movement of the radar carrier and the target, as having the greatest measure of uncertainty ( entropy) respectively among discrete and continuous distribution laws.

These features are essential and are not found in known technical solutions.

The use of all new essential features will make it possible to reliably identify the joint or separate impact of interference that leads away in range and speed with the simultaneous formation of reliable unconditional estimates of the distance to the CC and the speed of approach of the radar carrier to it by adaptive two-time parametric approximation of unknown probability densities of the FSK by a set of mixtures of a priori specified types of functions for by taking into account nonlinearities in the dynamics of the FGC and their measurements, taking into account the statistical dependence of the probabilities of changing the options for the effect of escaping interference from the FGC, integrating the information of the radar and the indicator (detector) of the variant of the effect of escaping interference, taking into account a priori data on the change of these options and adapting the surveillance system to them.

In FIG. Figure 2 shows a block diagram explaining the implementation of the proposed method for tracking an AT from the “aircraft with turbojet” class under the influence of interference that leads away in range and speed.

The method of tracking an AT from the class "aircraft with a turbojet engine" and identifying interference that leads away in range and speed is carried out as follows.

At the input of the well-known FFT block 1 used in [1], at an intermediate frequency from the output of the radar receiver, the signal S ₁ (t) is received, reflected from the CC, which is subjected to narrow-band Doppler filtering based on the FFT procedure and converted into an amplitude-frequency spectrum, components which are caused by signal reflections from the airframe of the accompanied AT and the rotating parts of the LPC of its power plant.

In the well-known measurement shaper 2 used in [1], firstly, the Doppler frequency reading F _p (k+1) is determined, corresponding to the maximum amplitude of the spectral component of the signal spectrum, which corresponds to its reflections from the CC airframe, and secondly, this reading Doppler frequency is converted into a speed value, as V _p (k+1) = λF _p (k+1)/2 (where λ is the operating wavelength of the radar), thirdly, the input range measurement in continuous time D(t ) is converted into discrete range readings D(k+1), fourthly, the Doppler frequency reading F _to (k+1) is determined, corresponding to the maximum amplitude of the spectral component of the signal spectrum, located to the right of the Doppler frequency relative to the spectral component of the signal reflected from the airframe VC, fifthly, this reading of the Doppler frequency is converted into a velocity value, as V _k (k + 1) \u003d λF _k (k + 1) / 2.

,

,

условиях 8 и множестве (Φ, Ψ, Θ, P, F) наборов видов аппроксимирующих функций 9, также поступающих на вход многоканального фильтра 28, 29, 30, 31.As a result, at the output of block 2, a measurement z _k+1 = (D(k+1), V _p (k+1), V _k (k+1)) ^{T is formed,} which, together with the output readings of indicator 2a, is fed to the input of a new multichannel filters 28, 29, 30, 31 for joint estimation of the radial distances to the CC, glider and compressor components of the radial velocity and acceleration of the relative movement of the radar carrier and the target, a filter, each channel of which operates in accordance with the well-known procedure of quasi-optimal joint filtering of phase coordinates and conditional recognition of the state -Markovian structure of a nonlinear stochastic dynamical system under observation without delay, whose block diagram and description are given in [3], and differs only in the variant of the set of approximating functions underlying this procedure. The multi-channel filter operates on the basis of a priori data (69)-(74) in the form of an MM system "VC - radar - indicator" with CCC, including (on-board computer memory unit 10) a nonlinear model of the dynamics of radial FSK 3 of the mutual movement of the carrier of the radar and CC, presented function, the model of their measurements in the radar 4, represented by the function ϕ _k (⋅), the model of changing the variant of the effect of escaping interference 5, represented by the transition probabilities q _k (⋅), the model of the indicator of the variant of the impact of escaping interference 6, represented by the transition probabilities π _k+1 (⋅ ), a model of uncontrolled random perturbations and noise 7, represented by a joint distribution function Φ _k (⋅), with initial ƒ ₀ (x ₀ , s ₀ ),

,

,

conditions 8 and the set (Φ, Ψ, Θ, P, F) of sets of types of approximating functions 9, also fed to the input of the multichannel filter 28, 29, 30, 31.

,

,

воздействия уводящих помех по каждому варианту при фиксированном варианте набора аппроксимирующих функций, условные математические ожидания ФСК

,

,

,

при фиксированных варианте набора аппроксимирующих функций и варианте воздействия уводящих помех, условные КМ ошибок оценивания ФСК

,

,

,

при фиксированных варианте набора аппроксимирующих функций и варианте воздействия уводящих помех, поступают на вход нового классификатора варианта набора аппроксимирующих функций 22, функционирующего в соответствии с (50), на вход которого также с блока 10 памяти бортовой ЦВМ поступают априорные данные в виде аппроксимированной модели индикатора варианта воздействия уводящих помех 6, множества наборов видов аппроксимирующих функций 9 и начальных

вероятностей 8 соответствия вариантов набора аппроксимирующих функций фактическим видам, с вычислителя обратного преобразования Фурье от характеристической функции измерения 18 поступает условная плотность вероятности

, с формирователя 2 поступают результаты измерения ФСК z_k+1, с индикатора 2а варианта воздействия уводящих помех поступают его выходные показания r_k+1, а также поступают вероятности

соответствия вариантов набора аппроксимирующих функций фактическим видам закономерностей, рассчитанные для предыдущего шага дискретности.Probabilities formed at the output of the multichannel filter 28, 29, 30, 31

,

,

effects of diverting interference for each variant with a fixed variant of the set of approximating functions, conditional mathematical expectations of the FGC

,

,

,

with a fixed variant of the set of approximating functions and the variant of the influence of diverting noise, conditional KM of estimation errors of the FSK

,

,

,

with a fixed variant of the set of approximating functions and the variant of exposure to diverting interference, they are fed to the input of a new classifier of the variant of the set of approximating functions 22, functioning in accordance with (50), to the input of which a priori data are also received from the memory block 10 of the onboard computer in the form of an approximated model of the indicator of the variant effects of escaping interference 6, a set of sets of types of approximating functions 9 and initial

probabilities 8 of correspondence of options for a set of approximating functions to actual types, from the calculator of the inverse Fourier transform from the characteristic function of measurement 18 comes the conditional probability density

, from the shaper 2 the results of the measurement of the FSK z _k+1 are received, from the indicator 2a of the variant of the effect of diverting interference, its output readings r _k+1 are received, and also the probabilities

correspondence of variants of the set of approximating functions to the actual types of regularities calculated for the previous step of discreteness.

соответствия вариантов набора аппроксимирующих функций фактическому виду закономерностей взаимного перемещения носителя РЛС и ВЦ, которые поступают на вход нового идентификатора варианта набора аппроксимирующих функций 23, функционирующего в соответствии с (51)-(56), нового смесителя аппроксимирующих функций 24, функционирующего в соответствии с (57)-(61), нового безусловного по отношению к вариантам набора аппроксимирующих функций идентификатора 25 варианта воздействия уводящих помех, функционирующего в соответствии с (62), нового безусловного по отношению к вариантам набора аппроксимирующих функций фильтра ФСК 26, функционирующего в соответствии с (63), и нового безусловного по отношению к вариантам набора аппроксимирующих функций дисперсиометра ФСК 27, функционирующего в соответствии с (64).As a result, at the output of block 22, probabilities are formed

correspondence of the variants of the set of approximating functions to the actual form of the patterns of mutual movement of the carrier of the radar and the computer center, which are fed to the input of the new identifier of the variant of the set of approximating functions 23, functioning in accordance with (51)-(56), the new mixer of approximating functions 24, functioning in accordance with ( 57)-(61), a new unconditional with respect to the options set of approximating functions of the identifier 25 of the variant of the effect of diverting interference, functioning in accordance with (62), a new unconditional with respect to the options set of approximating functions of the filter FSK 26, functioning in accordance with (63 ), and a new set of approximating functions of the FSK 27 dispersiometer, unconditional with respect to the variants, operating in accordance with (64).

,

,

,

воздействия уводящих помех по каждому варианту при фиксированном варианте набора аппроксимирующих функций, условные математические ожидания ФСК

,

,

,

при фиксированном варианте набора аппроксимирующих функций и условные КМ ошибок оценивания ФСК

,

,

,

при фиксированном варианте набора аппроксимирующих функций. Также на вход дисперсиометра 27 поступают апостериорные условные математические ожидания ФСК

,

,

при фиксированном варианте набора аппроксимирующих функций и найденное в безусловном фильтре 26 математическое ожидание ФСК

.In addition, the inputs of the identifier 23 and the mixer 24 receive sets Φ, Ψ, Θ, P and F of the types of approximating functions 9, and the inputs of the identifier 25, filter 26 and dispersion meter 27 from the outputs of the multichannel filter 28, 29, 30, 31 probabilities

,

,

,

effects of diverting interference for each variant with a fixed variant of the set of approximating functions, conditional mathematical expectations of the FGC

,

,

,

for a fixed variant of the set of approximating functions and conditional KMs of FSK estimation errors

,

,

,

for a fixed set of approximating functions. Also, the input of the dispersion meter 27 receives a posteriori conditional mathematical expectations of the FGC

,

,

for a fixed version of the set of approximating functions and the mathematical expectation of FSK found in the unconditional filter 26

.

варианта набора аппроксимирующих функций, на выходе смесителя 24 оценка

варианта набора аппроксимирующих смесей, на выходе идентификатора 25 оценка

варианта воздействия уводящих помех, на выходе фильтра 26 оценка

математического ожидания ФСК, на выходе дисперсиометра 27 оценка КМ ошибок оценивания ФСК поступают на выход канала сопровождения ВЦ в РЛС.Formed output id 23 score

variant of a set of approximating functions, at the output of the mixer 24 score

variant of a set of approximating mixtures, at the output of the identifier 25 score

variant of influence of the leading interference, at the output of the filter 26 rating

mathematical expectation of the FSK, at the output of the dispersion meter 27, the estimate of the KM of the estimation errors of the FSK is fed to the output of the tracking channel of the CC in the radar.

, построенных по исходным данным табл. 3.In FIG. Figure 3 shows an example of a family of probability densities of beta (Fig. 1) and gamma (Fig. 2) distributions (the values of the distribution parameters are presented in Tables 1 and 2, respectively), which are considered as elements of the set F of alternative conditional probability densities of the FGC at a fixed the variant of the effect of diverting noise (38), as well as specific implementations of these alternative approximating densities (Fig. 3, 5, 7, 9) and the corresponding families of mixtures (87 g) from these densities (Fig. 4, 6, 8, 10) for different probabilities

, constructed according to the initial data of Table. 3.

The probability density of the beta distribution, generalized to the case of an arbitrary segment [c;d], with the necessary expressions for the distribution parameters in terms of conditional MO and variance, are determined by the relations

and the probability density of the gamma distribution has the form

where

вектора ФСК и дисперсии

ошибки ее оценивания при фиксированном варианте s_k воздействия уводящих помех; a {s _k ) and b(s _k ) are parameters of the beta distribution depending on the conditional MO component

FSK vector and variance

the error of its estimation for a fixed variant s _{k of the} effect of diverting interference;

c and d are, respectively, the left and right boundaries of the possible values of the considered component of the FGC vector;

B( a (s _k ),b(s _k )) - beta function;

вектора ФСК и дисперсии

ошибки ее оценивания при фиксированном варианте воздействия уводящих помех s_k;α(s _k ) and β(s _k ) - parameters of the gamma distribution, depending on the conditional MO component

FSK vector and variance

errors of its estimation at the fixed variant of influence of the leading noises s _k ;

Г(α(s _k )) - gamma function.

In this case, the essence of the procedure of quasi-optimal joint filtering of phase coordinates and recognition of the state of the conditionally Markov structure of a nonlinear stochastic dynamical system is as follows.

,

аппроксимирующих функций, удовлетворяющих условиям нормировки (30), (33), (35), (37) и обеспечивающих (40) при их подстановке в (1)-(6), (10), (17)-(20) выражение интегралов алгоритма через элементарные или табулированные функции. При этом для аппроксимации условной плотности вероятности

ФСК при фиксированном варианте воздействия уводящих помех выбираются такие функции

,

параметры которых зависят не более чем от первых двух вероятностных моментов - вектора условных МО

фазовых координат и условных КМ

ошибок их оценивания, и связаны с ними простыми алгебраическими соотношениями, например бета- и гамма- распределения (75), (76), представленные на фиг. 3, рис. 1, 2.1. On the basis of a priori data presented by the MM of the system "CC - radar - indicator" (69) - (74), put forward (28), (31), (34), (36), (38) hypothesis Г about alternative types

,

approximating functions that satisfy the normalization conditions (30), (33), (35), (37) and provide (40) when they are substituted into (1)-(6), (10), (17)-(20) the expression integrals of the algorithm through elementary or tabulated functions. In this case, to approximate the conditional probability density

FSK with a fixed variant of the effect of eavesdropping interference, the following functions are chosen:

,

whose parameters depend on no more than the first two probabilistic moments - the vector of conditional MOs

phase coordinates and conditional KM

errors in their estimation, and are related to them by simple algebraic relations, for example, beta and gamma distributions (75), (76), presented in Fig. 3, fig. 12.

воздействия уводящих помех по каждому варианту при фиксированном варианте набора аппроксимирующих функций, условных МО

функционально-связанных координат и КМ

ошибок их оценивания при фиксированных варианте набора аппроксимирующих функций и варианте воздействия уводящих помех.2. The system of equations closes and complex integral recurrent equations (1)-(27) degenerate into new ordinary recurrent equations (41)-(65) with respect to conditional probabilities

effects of diverting interference for each variant with a fixed variant of the set of approximating functions, conditional MO

functionally related coordinates and KM

errors of their estimation for a fixed variant of the set of approximating functions and the variant of the effect of diverting noise.

воздействия уводящих помех, МО

функционально-связанных координат и КМ

ошибок их оценивания при фиксированном варианте набора аппроксимирующих функций.3. In accordance with expressions (41)-(49), conditional quasi-optimal according to the criterion of maximum a posteriori probability estimates of the variant are found

effects of eavesdropping interference, MO

functionally related coordinates and KM

errors in their estimation for a fixed set of approximating functions.

соответствия варианта набора аппроксимирующих функций фактическому виду закономерностей взаимного перемещения носителя РЛС и ВЦ.4. Taking into account the hypothesis put forward, in accordance with (50), the a posteriori probabilities are found

correspondence of the variant of the set of approximating functions to the actual form of the patterns of mutual movement of the radar carrier and the CC.

смесей аппроксимирующих функций из априорно задаваемых множеств таких функций, взятых с весовыми коэффициентами, пропорциональными вероятностям

соответствия видов этих функций видам фактических закономерностей взаимного перемещения носителя РЛС и ВЦ.5. Taking into account the hypothesis put forward and the probabilities found, in accordance with (57) - (61), a set of models of the dynamics of the FSK, their measurements in the radar, the change in options for the effect of escaping interference, the indicator of such options and the conditional probability density of the FSK under a fixed variant of the impact of escaping interference are estimated , set

mixtures of approximating functions from a priori given sets of such functions, taken with weight coefficients proportional to the probabilities

the correspondence of the types of these functions to the types of actual patterns of mutual movement of the carrier of the radar and CC.

и

при фиксированном варианте набора аппроксимирующих функций, и апостериорных вероятностей

соответствия наборов видов этих функций видам фактических закономерностей, в соответствии с (62)-(64) находятся безусловные, по отношению к вариантам набора аппроксимирующих функций, квазиоптимальные по критерию максимума апостериорной вероятности оценки варианта

воздействия уводящих помех, МО

функционально-связанных координат и КМ

ошибок их оценивания.6. Taking into account the found conditional estimates

and

for a fixed set of approximating functions, and a posteriori probabilities

correspondence of the sets of types of these functions to the types of actual regularities, in accordance with (62)-(64) are unconditional, with respect to the variants of the set of approximating functions, quasi-optimal according to the criterion of maximum a posteriori probability of estimating the variant

effects of eavesdropping interference, MO

functionally related coordinates and KM

errors in their evaluation.

7. In the absence of additional a priori data, the initial conditions for the probabilities of the influence of eavesdropping interference according to the fixed variant are assumed to be equally probable (66), and for the MO of functionally related coordinates and the CM of their estimation errors - uniform (67), (68), as having the highest entropy .

On fig. 4, 6, 8, 10 show the final approximating mixtures from beta and gamma distributions taken with weighting coefficients from Table. 3.

The results of comparative modeling of the proposed method of tracking ATs from the class "aircraft with turbojet engines" under the influence of noise that leads away in range and speed based on a multi-channel filter for joint estimation of the radial range to the target, glider and compressor components of the radial velocity and acceleration of the mutual movement of the radar carrier and the target, and recognition variant of the effect of diverting interference, functioning in accordance with the procedure of quasi-optimal joint filtering of phase coordinates and recognition of the state of the conditionally Markov structure of a nonlinear stochastic dynamic system during observation without delay based on an adaptive two-time parametric approximation of unknown probability densities by a mixture of a priori specified approximating functions, and a well-known method for tracking the CC from the class "aircraft with a turbojet engine" under the influence of interference that leads away in range and speed [2] indicate with a confidence probability of 0.99 a decrease in the RMS error of the fil correction by 9 ± 0.1% and an increase in the probability of correctly recognizing the variant of the effect of diverting interference by 8 ± 0.1%.

Thus, the application of the proposed invention will improve the reliability of the joint or separate effects of escaping interference and estimates of the radial functionally related range to the CC and the speed of approach of the radar carrier with it by adaptive two-time parametric approximation of unknown probability densities with a mixture of a priori specified approximating functions and approximation of the resulting estimates to their optimal values by taking into account non-linearities in the FSK dynamics and their measurements, taking into account the statistical dependence of the probabilities of changing options for the effects of fading interference from the FSK, integrating the information of the radar and the indicator of the variant of the effect of fading interference, taking into account a priori data on the change of these options and adapting the surveillance system to them.

SOURCES OF INFORMATION

1. Bogdanov A.V., Vasiliev O.V., Dokuchaev Ya.S. A method for tracking an air target from the "aircraft with a turbojet engine" class under the influence of interference that leads away in range and speed. Patent for invention No. 2665031, 2018 (analogue).

2. Muzhichek S.M., Filonov A.A., Skrynnikov A.A., Fedotov A.Yu., Tkacheva O.O., Vikulova Yu.M., Kornilov A.A., Makashin S.L. A method for tracking an air target from the "aircraft with a turbojet engine" class under the influence of interference that leads away in range and speed. Patent for invention No. 2713635 dated 05.02.20 (prototype).

3. Bukhalev, V.A. Optimal smoothing in systems with random jump structure / V.A. Bukhalev. Moscow: FIZMAT LIT, 2013, pages 115, 116, 117.

Claims (1)

A method for tracking an air target from the "aircraft with a turbojet engine" class under the influence of interference that leads away in range and speed, which consists in the fact that the signal reflected from the target is subjected to narrow-band Doppler filtering based on the fast Fourier transform procedure and converted into an amplitude-frequency spectrum, the components of which are due to signal reflections from the glider of the tracked air target (AT) and the rotating blades of the impeller of the low-pressure compressor of its power plant, the Doppler frequency count corresponding to the maximum amplitude of the spectral component of the signal spectrum, which corresponds to its reflections from the VT glider, and the Doppler frequency count are determined , corresponding to the maximum amplitude of the spectral component of the signal spectrum, located to the right in the Doppler frequency relative to the spectral component of the signal reflected from the airframe CC, characterized in that the selected samples of the Doppler frequencies along step at the input of the multichannel filter of joint tracking of the EC and the first compressor component of the signal spectrum and identification of the variant of the effect of diverting interference, functioning in accordance with the procedure of quasi-optimal joint filtering of phase coordinates and recognition of the state of the conditionally Markov structure of a nonlinear stochastic dynamic system during observation without delay, a procedure based on on a priori data in the form of a mathematical model (MM) of the "air target - radar station - indicator" system with a random jump structure (SSS), including, in general, a nonlinear model of the dynamics of radial functionally related coordinates (FCC), which refers to the range to the target, glider and compressor components of the radial velocity and acceleration of the mutual movement of the carrier of the radar station (RS) and CC, a nonlinear model for measuring these phase coordinates in the radar, a conditionally Markov model for changing the options for the impact of the withdrawal induced interference, a conditional Markov model of the indicator of the variant of the effect of stray interference, a model of uncontrolled random perturbations and interference, under initial conditions, based on a priori data, a statistical hypothesis is put forward about the options for a set of approximating functions, to approximate the conditional probability density of phase coordinates for a fixed variant of the impact of stray interference, such functions whose parameters depend on no more than the first two probabilistic moments (vectors of conditional mathematical expectations of phase coordinates and covariance matrices of their estimation errors) and are related to them by simple algebraic relations, the system of equations closes and complex integral recurrent equations degenerate into ordinary recurrent equations with respect to conditional probabilities of the effect of escaping interference for each variant with a fixed variant of the set of approximating functions, conditional mathematical expectations (MO) of phase coordinates and covariance m matrixes (QM) of their estimation errors for a fixed variant of the set of approximating functions and the variant of the effect of escaping interference, based on a priori data on the change in the variant of the effect of escaping interference and the dynamics of phase coordinates, represented respectively by the initial and transition probabilities of the conditional Markov chain and the FGC dynamics model, according to the results measurements with alternative models corresponding to different variants of the effect of stole interference, and the indications of the indicator of the variant of the effect of stole interference with the corresponding model, joint estimation of the FSK and identification of the variant of the effect of staggering interference are carried out in several quasi-optimal filters that are multichannel in terms of the number of considered options for the effect of stooping interference, differing in the variant of the set of approximating functions , while in each filter, based on a priori data on the change in the options for the effect of diverting interference, represented respectively by the initial and transition probabilities of the conditional circuit Markov, the probabilities of the effect of escaping interference for each variant are predicted by one discrete step forward with a fixed variant of the set of approximating functions, taking into account the found probabilities based on a priori data on the change in the options for the effect of escaping interference and the dynamics of the FGC of the mutual movement of the carrier of the radar and AT, taking into account the found, as the inverse Fourier transform of the characteristic function of the phase coordinates, the conditional probability density of the FSK and its approximating function, the conditional mathematical expectations of the FSK are predicted one step forward for a fixed variant of the set of approximating functions and the variant of the influence of diverting noise, taking into account the found probabilities and the MO are predicted by one step forward discreteness conditional KM of estimation errors of the FSK for a fixed variant of the set of approximating functions and the variant of the influence of diverting interference, according to the degree of consistency represented by the likelihood function, predicted probabilities, The MO of functionally related coordinates and the CM of their estimation errors with the measurement results and indicator readings, taking into account the conditional probability density of these measurements and its approximating function, found as the inverse Fourier transform of the measurement characteristic function, and its approximating function, the a posteriori probabilities of the effect of escaping interference are estimated for each variant at a fixed variant of the set of approximating functions, for each alternative measurement model corresponding to different variants of the effect of escaping interference, based on the predicted MO and CM forecast errors, taking into account the measurement results and indicator readings, conditional a posteriori functions, for each alternative measurement model corresponding to different options for the effects of eavesdropping interference, based on the predicted MO and CM prediction errors, taking into account the measurement results and of the indicator readings, the conditional a posteriori CMs of FSK filtering errors are estimated for a fixed form of the approximating function, from the possible options for the effect of escaping interference, the one for which, with a fixed version of the set of approximating functions, the estimated a posteriori probability will be greater, unconditional with respect to the options for the impact of escaping interference, the estimate of the FSK for a fixed variant of a set of approximating functions is calculated on the basis of a posteriori probabilities of the effect of escaping interference for each variant and conditional a posteriori estimates of the FSK, as an unconditional MO, taking into account the a posteriori probabilities of the effect of escaping interference for each variant, conditional mathematical expectations of the FGC, conditional KM of errors in their estimation and unconditional assessment FSK is found unconditional with respect to the options for the impact of the KM of estimating errors of the FSK estimation errors for a fixed version of the set of approximating functions, for each of the multichannel ones, by the number to the variants of the effect of diverting noise, filters that differ in the variant of the set of approximating functions, in terms of the degree of consistency represented by the likelihood function, predicted probabilities, mathematical expectations of the FGC and CM of their estimation errors with a fixed variant of the set of approximating functions with the results of regular measurements and indicator readings, taking into account the found , as the inverse Fourier transform of the characteristic function of measurements, the conditional probability density of these measurements and its approximating function, the a posteriori probabilities of the correspondence of the options for the set of approximating functions from their given sets to the actual form of the patterns of mutual movement of the carrier of the radar and CC are corrected, from the possible options for the set of approximating functions, the one is identified for which the corrected probability turns out to be greater, a set of models is estimated according to the dynamics of the FSK, their measurements in the radar station, the change in the air variant the effects of decoy interference, the indicator of the effect of decoy interference and the conditional probability density of the FSK under a fixed variant of the effect of decoy interference, by a set of mixtures of approximating functions from a priori specified sets, taken with weight coefficients proportional to the probabilities of the correspondence of the types of these functions to the actual type of patterns of mutual movement and interaction of the radar carrier and CC, taking into account the found estimates of the probabilities of the correspondence of sets of types of approximating functions to the actual type of patterns of mutual movement and interaction of the carrier of the radar and CC, and a posteriori conditional probabilities of the effect of escaping interference for each option with a fixed variant of the set of approximating functions, the variant of the effect of escaping interference is identified, taking into account the found conditional estimates of the FGC for a fixed version of the set of approximating functions and the probabilities that the variants of the set of these functions correspond to the actual form of the patterns of mutual reversal displacement and interaction of the radar carrier and the CC, the assessment of the FSK is determined as unconditional, in relation to the options for the set of approximating functions, mathematical expectation, taking into account the found a posteriori probabilities of the correspondence of the options for the set of approximating functions to the actual types of patterns of mutual movement and interaction of the radar carrier and the CC, conditional mathematical expectations of FSK and QM of their estimation errors for a fixed variant of the set of approximating functions, and unconditional estimates of these FSK, unconditional with respect to the options for the set of approximating functions of the QM of estimation errors of the FSK, initial conditions, in the absence of additional a priori data, respectively, for the variant of the set of approximating functions, variant effects of escaping interference and FSK of the mutual movement of the carrier of the radar and CC are taken, respectively, equiprobable and uniform, as having the largest measure of uncertainty (entropy) among the discrete and continuous distribution laws niya.

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